Transcript Synchronous machines

SYNCHRONOUS MACHINES
SUBMITTED BY:
Ms. APOORVA KANTHWAL
ASST. PROFESSOR-EEE
Synchronous machines are AC machines that have a field circuit
supplied by an external DC source.
In a synchronous generator, a DC current is applied to the rotor winding
producing a rotor magnetic field. The rotor is then turned by external means
producing a rotating magnetic field, which induces a 3-phase voltage within the
stator winding.
In a synchronous motor, a 3-phase set of stator currents produces a rotating
magnetic field causing the rotor magnetic field to align with it. The rotor
magnetic field is produced by a DC current applied to the rotor winding.
Field windings are the windings producing the main magnetic field (rotor
windings for synchronous machines); armature windings are the windings where
the main voltage is induced (stator windings for synchronous machines).
The rotor of a synchronous machine is a large electromagnet. The magnetic poles can be
either salient (sticking out of rotor surface) or non-salient construction.
Non-salient-pole rotor: usually two- and four-pole rotors.
Rotors are made laminated to reduce eddy current losses.
Salient-pole rotor: four
and more poles.
Two common approaches are used to supply a DC current to the field circuits on the
rotating rotor:
1. Supply the DC power from an external
DC source to the rotor by means of slip
rings and brushes;
2. Supply the DC power from a special DC
power source mounted directly on the
shaft of the machine.
Slip rings are metal rings completely encircling the shaft of a machine but insulated from it.
One end of a DC rotor winding is connected to each of the two slip rings on the machine’s
shaft. Graphite-like carbon brushes connected to DC terminals ride on each slip ring
supplying DC voltage to field windings regardless the position or speed of the rotor.
Slip rings
Brush
Slip rings and brushes have certain disadvantages: increased friction and wear
(therefore, needed maintenance), brush voltage drop can introduce significant power
losses. Still this approach is used in most small synchronous machines.
On large generators and motors, brushless exciters are used.
A brushless exciter is a small AC generator whose field circuits are mounted on
the stator and armature circuits are mounted on the rotor shaft. The exciter
generator’s 3-phase output is rectified to DC by a 3-phase rectifier (mounted on
the shaft) and fed into the main DC field circuit. It is possible to adjust the field
current on the main machine by controlling the small DC field current of the
exciter generator (located on the stator).
Since no mechanical contact occurs between the rotor and the stator, exciters of this
type require much less maintenance.
By the definition, synchronous generators produce electricity whose frequency
is synchronized with the mechanical rotational speed.
nm P
fe 
120
Where
(7.11.1)
fe is the electrical frequency, Hz;
nm is mechanical speed of magnetic field (rotor speed for synchronous
machine), rpm;
P is the number of poles.
Steam turbines are most efficient when rotating at high speed; therefore, to
generate 60 Hz, they are usually rotating at 3600 rpm and turn 2-pole
generators.
Water turbines are most efficient when rotating at low speeds (200-300 rpm);
therefore, they usually turn generators with many poles.
The magnitude of internal generated voltage induced in a given stator is
EA  2 NC f  K
where K is a constant representing the construction of the machine,  is flux in it and 
is its rotation speed.
Since flux in the
machine depends
on the field current
through it, the
internal generated
voltage is a function
of the rotor field
current.
Magnetization curve (open-circuit characteristic) of a
synchronous machine
The internally generated voltage in a single phase of a
synchronous machine EA is not usually the voltage appearing at its
terminals. It equals to the output voltage V only when there is no
armature current in the machine. The reasons that the armature
voltage EA is not equal to the output voltage V are:
1. Distortion of the air-gap magnetic field caused by the current
flowing in the stator (armature reaction);
2. Self-inductance of the armature coils;
3. Resistance of the armature coils;
4. Effect of salient-pole rotor shapes.
Armature reaction (the largest
effect):
When the rotor of a synchronous
generator is spinning, a voltage EA
is induced in its stator. When a load
is connected, a current starts
flowing creating a magnetic field in
machine’s stator. This stator
magnetic field BS adds to the rotor
(main) magnetic field BR affecting
the total magnetic field and,
therefore, the phase voltage.
Lagging
load
Assuming that the generator is connected to a lagging load, the load current IA will
create a stator magnetic field BS, which will produce the armature reaction voltage Estat.
Therefore, the phase voltage will be
V  E A  Estat
(7.16.1)
Bnet  BR  BS
(7.16.2)
The net magnetic flux will be
Rotor field
Stator field
Note that the directions of the net magnetic flux and the phase voltage are the same.
Assuming that the load reactance is X, the armature reaction voltage is
The phase voltage is then
Estat   jXI A
(7.17.1)
V  E A  jXI A
(7.17.2)
Armature reactance can be modeled by the following
circuit…
However, in addition to armature reactance effect, the
stator coil has a self-inductance LA (XA is the
corresponding reactance) and the stator has resistance
RA. The phase voltage is thus
V  E A  jXI A  jX A I A  RI A
(7.17.3)
Often, armature reactance and self-inductance are combined into the synchronous
reactance of the machine:
XS  X  X A
(7.18.1)
Therefore, the phase voltage is
V  E A  jX S I A  RI A
(7.18.2)
The equivalent circuit of a 3-phase
synchronous generator is shown.
The adjustable resistor Radj controls the field
current and, therefore, the rotor magnetic
field.
A synchronous generator can be Y- or -connected:
The terminal voltage will be
(7.19.1)
VT  3V  forY 
VT  V  for
(7.19.2)
Note: the discussion above assumed a balanced load on the generator!
Since – for balanced loads – the three phases of a synchronous generator are identical
except for phase angles, per-phase equivalent circuits are often used.
Since the voltages in a synchronous generator are AC voltages, they are usually expressed
as phasors. A vector plot of voltages and currents within one phase is called a phasor
diagram.
A phasor diagram of a synchronous generator with
a unity power factor (resistive load)
Lagging power factor (inductive load): a larger
than for leading PF internal generated voltage EA
is needed to form the same phase voltage.
Leading power factor (capacitive load).
For a given field current and magnitude of load
current, the terminal voltage is lower for lagging
loads and higher for leading loads.
A synchronous generator needs to be connected to a prime mover whose speed is
reasonably constant (to ensure constant frequency of the generated voltage) for various
loads.
The applied mechanical power
Pin   appm
(7.22.1)
is partially converted to electricity
Pconv   ind m  3EA I A cos 
Where  is the angle between EA
and IA.
The power-flow diagram of a
synchronous generator.
(7.22.2)
The real output power of the synchronous generator is
Pout  3VT I L cos   3V I A cos 
(7.23.1)
The reactive output power of the synchronous generator is
Qout  3VT I L sin   3V I A sin 
Recall that the power factor angle  is the angle between V and IA and not the angle
between VT and IL.
In real synchronous machines of any size, the
armature resistance RA << XS and, therefore, the
armature resistance can be ignored. Thus, a
simplified phasor diagram indicates that
E A sin 
I A cos  
XS
(7.23.3)
(7.23.2)
Then the real output power of the synchronous generator can be approximated as
Pout 
3V EA sin 
(7.24.1)
XS
We observe that electrical losses are assumed to be zero since the resistance is neglected.
Therefore:
Pconv  Pout
(7.24.2)
Here  is the torque angle of the machine – the angle between V and EA.
The maximum power can be supplied by the generator when  = 900:
Pmax 
3V E A
XS
(7.24.3)
The maximum power specified by (7.24.3) is called the static stability limit of the
generator. Normally, real generators do not approach this limit: full-load torque
angles are usually between 150 and 200.
The induced torque is
 ind  kBR  BS  kBR  Bnet  kBR Bnet sin 
(7.25.1)
Notice that the torque angle  is also the angle between the rotor magnetic field BR
and the net magnetic field Bnet.
Alternatively, the induced torque is
 ind 
3V E A sin 
m X S
(7.25.2)
The three quantities must be determined in order to describe the generator model:
1. The relationship between field current and flux (and therefore between the field
current IF and the internal generated voltage EA);
2. The synchronous reactance;
3. The armature resistance.
We conduct first the open-circuit test on the synchronous generator: the generator is
rotated at the rated speed, all the terminals are disconnected from loads, the field
current is set to zero first. Next, the field current is increased in steps and the phase
voltage (whish is equal to the internal generated voltage EA since the armature current is
zero) is measured.
Therefore, it is possible to plot the dependence of the internal generated voltage on the
field current – the open-circuit characteristic (OCC) of the generator.
Since the unsaturated core of the machine has a
reluctance thousands times lower than the
reluctance of the air-gap, the resulting flux increases
linearly first. When the saturation is reached, the
core reluctance greatly increases causing the flux to
increase much slower with the increase of the mmf.
We conduct next the short-circuit test on the synchronous generator: the generator is
rotated at the rated speed, all the terminals are short-circuited through ammeters, the
field current is set to zero first. Next, the field current is increased in steps and the
armature current IA is measured as the field current is increased.
The plot of armature current (or line current) vs. the field current is the short-circuit
characteristic (SCC) of the generator.
The SCC is a straight line since, for the shortcircuited terminals, the magnitude of the
armature current is
IA 
EA
RA2  X S2
(7.28.1)
The equivalent generator’s circuit during SC
The resulting
phasor diagram
Since BS almost cancels BR, the net
field Bnet is very small.
The magnetic fields
during short-circuit
test
An approximate method to determine the synchronous reactance XS at a given field
current:
1. Get the internal generated voltage EA from the OCC at that field current.
2. Get the short-circuit current IA,SC at that field current from the SCC.
3. Find XS from
XS 
EA
(7.29.1)
I A, SC
Since the internal machine impedance is
ZS  R  X 
2
A
2
S
EA
I A,SC
 X S since X S
RA 
(7.29.2)
A drawback of this method is that the internal generated voltage EA is measured during
the OCC, where the machine can be saturated for large field currents, while the armature
current is measured in SCC, where the core is unsaturated. Therefore, this approach is
accurate for unsaturated cores only.
The approximate value of synchronous
reactance varies with the degree of
saturation of the OCC.
Therefore, the value of the synchronous
reactance for a given problem should be
estimated at the approximate load of the
machine.
The winding’s resistance can be
approximated by applying a DC voltage to
a stationary machine’s winding and
measuring the current. However, AC
resistance is slightly larger than DC
resistance (skin effect).